In a large skillet, heat the olive oil over medium heat. Add the diced onion and cook until translucent, about 3-4 minutes. Then, add the minced garlic, cooking for an additional 1 minute.
Stir in the diced carrots and celery, cooking for 5-7 minutes until they start to soften. Add the ground beef, breaking it apart with a spatula. Cook until browned, about 5-6 minutes. Drain any excess fat.
To the skillet, add the frozen peas, beef broth, Worcestershire sauce, tomato paste, thyme, rosemary, salt, and pepper. Bring to a simmer and let it cook for 10 minutes, allowing the flavors to meld and the mixture to thicken slightly.
While the filling is simmering, roll out the puff pastry sheets on a lightly floured surface. Cut them into squares that will fit your baking dish (approximately 4x4 inches).
In a greased baking dish, place half of the pastry squares at the bottom. Pour the beef filling evenly over the pastry layer, then top with the remaining pastry squares.
In a small bowl, beat the egg and brush it over the top of the squares to give them a beautiful shine as they bake.
Place the baking dish in the preheated oven and bake for 25-30 minutes, or until the pastry is golden brown and puffed up.
Once baked, allow the pot pie squares to cool for a few minutes. Garnish with freshly chopped parsley before serving.
Serve your warm, comforting Beef Pot Pie Squares as a delightful family meal or whenever you're craving something hearty!